Problem Set #6: Building A Model - Goodman ✓ Solved

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Problem Set #6 Attached Files: Building a Model - Goodman

The attached file contains hypothetical data for working this problem. Goodman Corporation’s and Landry Incorporated’s stock prices and dividends, along with the Market Index, are shown in the file. Stock prices are reported for December 31 of each year, and dividends reflect those paid during the year. The market data are adjusted to include dividends. Use the data given to calculate annual returns for Goodman, Landry, and the Market Index, and then calculate average returns over the five-year period. Remember, returns are calculated by subtracting the beginning price from the ending price to get the capital gain or loss, adding the dividend to the capital gain or loss, and dividing the result by the beginning price. Assume that dividends are already included in the index. You cannot calculate the rate of return for 2015 because you do not have 2014 data. Calculate the standard deviation of the returns for Goodman, Landry, and the Market Index. Use the sample standard deviation formula given in the chapter, which corresponds to the STDEV function in Excel. On a stand-alone basis, which corporation is the least risky? Construct a scatter diagram graph that shows Goodman’s and Landry’s returns on the vertical axis and the Market Index’s returns on the horizontal axis. Estimate Goodman’s and Landry’s betas as the slopes of regression lines with stock returns on the vertical axis and market return on the horizontal axis. Are these betas consistent with your graph? The risk-free rate on long-term Treasury bonds is 8.04%. Assume that the market risk premium is 6%. What is the expected return on the market? Now use the SML equation to calculate the two companies' required returns. If you formed a portfolio that consisted of 60% Goodman stock and 40% Landry stock, what would be its beta and its required return? Suppose an investor wants to include Goodman Industries’ stock in his or her portfolio. Stocks A, B, and C are currently in the portfolio, and their betas are 0.769, 0.985, and 1.423, respectively. Calculate the new portfolio’s required return if it consists of 30% of Goodman, 20% of Stock A, 30% of Stock B, and 20% of Stock C.

Paper For Above Instructions

The analysis of Goodman Corporation and Landry Incorporated's stock performance over a period of five years reveals critical insights into their financial behaviors, including their returns, risk profiles, and required returns in the context of market evaluation.

Calculating Annual Returns

To begin with, we first calculate the annual returns for Goodman, Landry, and the Market Index. The formula used for calculating annual returns is given by:

Annual Return = (Ending Price - Beginning Price + Dividend) / Beginning Price

Assuming we have the required data from the file for each year, we can derive the annual returns for each entity. To find the average annual return over the five-year period, we accumulated these yearly returns and divided by five.

Standard Deviation of Returns

Next, we compute the standard deviation of the returns, which measures the volatility or risk associated with each stock. Using Excel's STDEV function applies the sample standard deviation formula, which is appropriate for our calculation given financial returns.

If we compute the standard deviations and compare them, we can determine which of Goodman or Landry is less risky on a stand-alone basis. The one with the lower standard deviation of returns is considered less risky.

Scatter Diagram and Beta Estimation

We then construct a scatter diagram to visualize the relationship between Goodman’s and Landry’s returns plotted against the Market Index returns. Utilizing regression analysis, the beta coefficients for both companies are calculated based on the slope of the regression lines that represent their stock returns against market returns. The formula for beta is generally expressed as:

Beta = Covariance (Stock Return, Market Return) / Variance (Market Return).

After determining these beta values, we must verify whether they align with the trends observed in our scatter plot.

Market and Required Returns

The next step entails calculating the expected return on the market using the formula:

Expected Market Return = Risk-free Rate + Market Risk Premium.

Using the given risk-free rate of 8.04% and a market risk premium of 6%, the expected market return can be easily computed as:

Expected Market Return = 8.04% + 6% = 14.04%.

Now, applying the Security Market Line (SML) model, we derive the required returns for Goodman and Landry using their respective betas.

Portfolio Analysis

Considering a portfolio with 60% Goodman stock and 40% Landry stock, we compute the overall beta of the portfolio:

Portfolio Beta = (Weight of Goodman  Beta of Goodman) + (Weight of Landry  Beta of Landry).

Finally, for an investor including Goodman Industries’ stock alongside Stocks A, B, and C (with known betas of 0.769, 0.985, and 1.423, respectively), we determine the new portfolio’s required return by incorporating the weights of each stock:

New Portfolio Required Return = (Weight of Goodman  Required Return of Goodman) + (Weight of A  Required Return of A) +

(Weight of B  Required Return of B) + (Weight of C  Required Return of C).

This yields a comprehensive overview of how the inclusion of Goodman impacts the overall portfolio dynamics and helps in performing strategic asset allocation.

Conclusion

This analytical process serves as a robust methodology for evaluating stocks within an investment context, delivering vital insights on returns, risks, and strategic opportunities for portfolio optimization.

References

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  • Modigliani, F., & Miller, M. H. (1958). The Cost of Capital, Corporation Finance and the Theory of Investment. The American Economic Review.
  • Mackinlay, A. C. (1997). Event Studies in Economics and Finance. Journal of Economic Literature.
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  • Brealy, R. A., & Myers, S. C. (2011). Principles of Corporate Finance. McGraw-Hill Education.
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